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  1. Andrew Bacon (2013). Quantificational Logic and Empty Names. Philosophers' Imprint 13 (24).
    The result of combining classical quantificational logic with modal logic proves necessitism – the claim that necessarily everything is necessarily identical to something. This problem is reflected in the purely quantificational theory by theorems such as $\exists xt = x$; it is a theorem, for example, that something is identical to Timothy Williamson. The standard way to avoid these consequences is to weaken the theory of quantification to a certain kind of free logic. However, it has often been noted that (...)
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  2. John Bacon (1982). First-Order Logic Based on Inclusion and Abstraction. Journal of Symbolic Logic 47 (4):793-808.
  3. Ermanno Bencivenga (2002). Free Logics. In D. M. Gabbay & F. Guenthner (eds.), Handbook of Philosophical Logic, 2nd Edition. Kluwer. 147--196.
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  4. Newton C. A. da Costa & Otavio Bueno (1999). Quasi-Truth, Supervaluations and Free Logic. History and Philosophy of Logic 20 (3-4):215-226.
    The partial structures approach has two major components: a broad notion of structure (partial structure) and a weak notion of truth (quasi-truth). In this paper, we discuss the relationship between this approach and free logic. We also compare the model-theoretic analysis supplied by partial structures with the method of supervaluations, which was initially introduced as a technique to provide a semantic analysis of free logic. We then combine the three formal frameworks (partial structures, free logic and supervaluations), and apply the (...)
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  5. D. M. Gabbay & F. Guenthner (eds.) (2002). Handbook of Philosophical Logic, 2nd Edition. Kluwer.
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  6. Roderic A. Girle (1974). Possibility Pre-Supposition Free Logics. Notre Dame Journal of Formal Logic 15 (1):45-62.
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  7. Carl J. Posy (1982). A Free IPC is a Natural Logic: Strong Completeness for Some Intuitionistic Free Logics. Topoi 1 (1-2):30-43.
    IPC, the intuitionistic predicate calculus, has the property(i) Vc(A c /x) xA.Furthermore, for certain important , IPC has the converse property (ii) xA Vc(A c /x). (i) may be given up in various ways, corresponding to different philosophic intuitions and yielding different systems of intuitionistic free logic. The present paper proves the strong completeness of several of these with respect to Kripke style semantics. It also shows that giving up (i) need not force us to abandon the analogue of (ii).
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